The reason you fall under higher risk is because you are transferring or aggregating funds instead of just collecting. This means you could be prone to money laundering. The new paypal api (that's in beta, see x.com) allows transactions like this without you taking the holding/fraud risk. Its probably your best shot.
Outside of that, you could try to get arrangements with an escrow provider (like escrow.com) to handle the payment part of your transactions.
So had checked X.com - but discarded them. Because they don't work with credit card transactions yet - only PayPal. Which would mean at least half the transactions being lost...
I went through this same problem a while back. The hard part was the direct deposit, most companies didn't offer it. I finally ended up using http://www.achdirect.com/
I'm not sure I would recommend them - their support was horrible, and the dinged me with a $100 "hidden fee" - but they were the only company I found who had an API for both billing and direct deposit and it did end up working eventually. BrainTree rejected my app too.
I wrote a ruby active_merchant plugin to interface with ACHDirect - ping me if you want the source.
I'm about to implement Recurly http://www.recurly.com/ on my own site, on top of PayPal Website Payments Pro.
Recurly abstracts my gateway's API stuff and stores payment details so I'm not tied to my gateway - much like I wouldn't use a Comcast email address to have the freedom to change TV providers.
Worth a try. Note: I'm a potential customer of theirs and have no other affiliation.
I know of one company that can do this, I don't like advertising friends businesses (simply because you might think I promote them because they are my friends).
I've used their services for several years now and they are in for the long haul and seem to be doing pretty good.
Warning though:
1) they're not cheap
2) the requirements are stiff, a lot of applicants get rejected
3) you'll need a Dutch BV to even begin the acceptation process, this will cost you a bundle. Even then the application may be declined (that's not their call, but the banks / PaySquares).
If all that hasn't scared you off yet drop me a line.
If 'barmstrong's solution works for the amount of the deposits you are looking at then that might be an easier solution.
Have you talked to your bank about this ? Have you talked to VISA ?
They might be able to give you pointers about which parties can handle the functionality you are looking for, they usually keep pretty good tabs on their IPSPs and gateways so they should be able to tell you.
You need a "card not present" specialist, that understands ecommerce/tech startups. I highly recommend talking with JetPay (jetpay.com). They are the largest CNP payment processor, and they are an engineering company (even the CEO is an alpha programmer geek). Furthermore, they can integrate directly with you so you don't need a middleman (e.g. Authorize.Net). Their API and services support is outstanding -- see http://www.jetpay.com/cc_update.php for details. We just wish we'd found them a year earlier!
Can you elaborate on the PayPal isuses? Have you looked at PayPal Authorization & Capture? I am launching an equipment rental site and planning to use PayPal Authorization & Capture to help me take deposits.
Outside of that, you could try to get arrangements with an escrow provider (like escrow.com) to handle the payment part of your transactions.